Recent content by sroeyz

Hello. Let M,N be a connected smooth riemannian manifolds. I define the metric as usuall, the infimum of lengths of curves between the two points. (the length is defined by the integral of the norm of the velocity vector of the curve). Suppose phi is a homeomorphism which is a metric...

Can you please help me doing the calculations? I know the final answer is that the number of independent components is (n^2(n^2-1))/12 Can you please show me how to reach this result?

Hello, I wish to show that on 3-dimensional manifolds, the weyl tensor vanishes. In other words, I want to show that the curvature tensor, the ricci tensor and curvature scalar hold the relation Please, if anyone knows how I can prove this relation or refer to a place which proves the...

Hello, I wish to show that on 3-dimensional manifolds, the weyl tensor vanishes. In other words, I want to show that the curvature tensor, the ricci tensor and curvature scalar hold the relation Please, if anyone knows how I can prove this relation or refer to a place which proves the...

Hello, I seem to be having difficulty proving something. I hope you can help me. I will write del_X(Y) when I refer to the levi-chivita connection (used on Y in the direction of X). Let G be a lie group, with a bi-invariant metric , g , on G. I want to prove that del_X(Y) = 0.5 [X,Y]...